At age eleven Dainius moved to Kharkov, Ukraine to play hockey and became good friends with Dmitri Yakushin. The two friends would later find themselves teammates while playing junior hockey in Canada. The Canadian hockey scene was not an entirely new experience for Zubrus when he joined the Pembroke Lumber Kings in 1995 as he had been to Canada three years earlier to play in the 1992 Quebec International Pee Wee tournament.
Zubrus was drafted 15th overall in the 1996 NHL Entry Draft by the Philadelphia Flyers and he made his NHL debut on October 5, 1996, scoring a goal against the Florida Panthers. In his rookie season he proved that he could not be intimidated by the opposition and even earned some playing time on the Flyers big line with Eric Lindros and John LeClair, and helped the Flyers reach the Stanley Cup final only to lose in four straight games against the Detroit Red Wings.
The Flyers traded him to the Montreal Canadiens on March 10, 1999, with a pair of draft picks, for Mark Recchi. While in Montreal he took steps to improve his all-around game and had his best season, statistically speaking, in 1999-00. He registered his first career hat-trick on October 14, 2000, against the Chicago Blackhawks, but was traded by the Canadiens to the Washington Capitals on March 13, 2001, and finished the year 16 points off his previous best total.
The talented forward established a career high 43 points in 2001-02 and continued his strong play the following year despite being limited to a mere 63 games. In 2003-04 Zubrus reached the 500-games played plateau and was named to Team Russia for the 2004 World Cup of Hockey.
In 2005-06, Zubrus tallied a new career high 57 points in his 71 games the Capitals. The following season Zubrus would continue his assault offensively on the league alongside sophomore sensation Alexander Obvechkin. Despite his increased point production, Zubrus was dealt to the Buffalo Sabres with Timo Helbling for Jiri Novotny and a 1st-round draft pick.
Zubrus finished his season off with the Sabres recording a career-high 24 goals and 36 assists. After only 19 regular season, and 15 playoff games played with the Sabers, Zubrus' time in Buffalo had come to an end. The free agent Lithuanian was signed by the New Jersey Devils in the summer of 2007.
In the offseason of 2015, Zubrus was placed on waivers with the purpose of buying him out on July 29, 2015. After the start of the 2015-16 season, the San Jose Sharks signed Zubrus to a one year contract on November 24, 2015.